J . Am. Chem. SOC.1991, 113, 7147-7151
7147
Do the Vinyl Isomers of C2H2C1+and C2H2Br+Exist? Tracy P. Hamilton and Henry F. Schaefer III* Contribution from the Center for Computational Quantum Chemistry, University of Georgia, Athens. Georgia 30602. Received December 27, 1990
Abstract: Five stationary points on the potential energy hypersurfaces for the C2H2CI+and C2H2Br+cations are found at various levels of ab initio quantum-mechanical theory. At lower levels of theory, the vinyl-like cations are minima on the potential energy surface. Upon improvement of the wave function to include polarization functions and electron correlation, the structures corresponding to the classical 2-halovinyl cations become shallow minima or transition states. It is clear that both the halogen-bridged structure and the H2CCX+ isomer are stable minima that are lower in energy than HCCHX+, a fact not evident from low-level theory. This emphasizes that comparisons made between unsophisticated ab initio studies and experimental solution chemistry should be made with caution. Stabilization energies are evaluated for comparison with previous studies.
Introduction The study of vinyl cations as reactive intermediates has grown in the past two decades, with an entire volume dedicated to the subject.' These cationic species participate in the solvolysis of vinyl halides and vinyl triflates and are involved in electrophilic additions to acetylenes. In general, the addition of chlorine and bromine to double bonds is much faster than addition to triple bonds, especially in solvents with low dielectric constants.2 The addition of halogens to alkynes generates "vinyl cations" with either bridged or open structures. Given the importance of these cations in organic reaction mechanisms, it is of interest to know the inherent stabilities of the unsubstituted ions and the factors that affect the relative energies in the absence of solvent effects and alkyl or aryl substituents. Lucchini and Modena point out that the relative stability of bridged vs open ions is different between the saturated and unsaturated a n a l ~ g u e s .The ~ isomers containing three-membered rings are more viable in the saturated cases, although there is experimental evidence for halogen-bridged intermediates in dialkylacetylenes2 or diaryla~etylenes.~ Past theoretical studies have primarily focused on the parent vinyl cation, C2H3+,at high levels of theory (see ref 5 and references therein). Naturally, the most studied system in the halogen series is the C2H2Ft potential energy surface, but these studies have been performed only with small basis sets and without the inclusion of electron correlation@ or by semiempirical methods.I0 Similarly, C2H2CI+has been investigated by low-level a b initio theory9J'J2 and by MNDO.I3 Details from these papers will be covered when the corresponding topic arises under Results and Discussion. No experimental or theoretical papers on C2H2Br+ have appeared in the literature. This article reports on a b initio studies of the potential energy surfaces for C2H2CI+and C2H2Br+,with emphasis on the existence ( I ) Vinyl Cafions;Stang, P. J., Rappoport, Z., Hanack, M., Subramanian, L. R., Eds.; Academic: New York, 1979. (2) Yates, K.; Schmid, G. H.; Regulski, T. W.;Garrat, D. G.;Leung, H. W.;McDonald, R. J. Am. Chem. Soc. 1975, 75, 160. (3) Lucchini, V.; Modena, G. frog. Theor. Org. Chem. 1977, 2, 268. (4) Bassi, P.; Tonellato, U. J . Chem. SOC.,Perkin Trans. 2 1974, 1283. ( 5 ) Liang, C.; Hamilton, T. P.; Schaefer, H. F. J . Chem. Phys. 1990, 92, 3653. (6) Apeloig, Y.; Schleyer, P. v. R.; Pople, J. A. J . Am. Chem. SOC.1977,
and relative energies of the 1-halovinyl (H2CCX+), 2-halovinyl (HCCHX'), and bridged (halenium) ions. The basis sets used are more complete than in previous studies, and electron correlation will be accounted for by large-scale configuration interaction (CI) wave functions. The influence of inductive effects, back-donation from halogen lone pairs, and hyperconjugation is addressed, and the stabilization of the vinyl cation by C1 or Br (relative to H ) is also discussed. Theoretical Methodology The wave functions utilized throughout were the Hartree-Fock selfconsistent-field (SCF) and CI with single- and double-substitution (CISD) wave functions. The core orbitals were kept frozen (Is on C; Is, 2s, 2p on CI; Is, 2s, 2p, 3s, 3p, 3d on Br), as were virtual orbitals lying above 20 hartrees. The resulting numbers of frozen orbitals are given in Tabla I and 11. The approximate effect of quadruple excitations was incorporated by utilizing the Davidson correction." Geometry optimizations were performed by using analytic gradients for both SCFI5 and CISDI6 levels of theory. The location of transition states was accelerated by using the eigenvector-following routine of Baker." The stationary points on the SCF potential energy surfaces were characterized as minima or transition states by harmonic vibrational frequency analyses based on analytically computed second derivatives.Is Likewise, IR intensities were obtained from analytic dipole moment derivatives. Three levels of basis set quality were used, namely double-{ (DZ), DZ with a set of polarization d functions on each heavy atom (DZ+d), and triple-{ with two sets of polarization functions of heavy atoms combined with a set of p polarization functions appended to the hydrogen DZ basis. The last basis will be referred to as TZ2P for brevity, even though it is of only DZP quality on the hydrogen atoms. All of the d function sets were five-component spherical harmonics. The DZ basis consisted of the standard contracted set from Huzinaga and Dunning for carbon (9s5p/4s2p) and hydrogen (4~/2s),I~*~O the ( I ls7p/6s4p) Huzinaga-Dunning set for C1,2' and the Br (15s12p5d/ 8s6p2d) set from Dunning that was tabulated in ref 22. The exponents of the polarization d functions were ad(C) = 0.75, ad(CI) = 0.75, and ad(Br) = 0.40 in the DZ+d basis. The sp part of the TZ2P basis consisted of the Huzinaga-Dunning (IOs6p/5s3p) set for c a r b ~ n , Ithe ~*~~ and thc McLean-Chandler (1 2s9p/6sSp) contracted Gaussians for
99, 1291. (7) Apeloig, Y.; Schleyer, P. v. R.; Pople, J. A. J. Am. Chem. SOC.1977, 99, 5901. (8) Csizmadia, I. G.; Lucchini, V.; Modena, G. Theor. Chim. Acta. 1975, 39, 51. (9) Martin, P. S.; Yates, K.;Csizmadia, I. G. Can. J. Chem. 1989, 67,
(14) Davidson, E. R. In The World OjQuantum Chemistry; Daudel, R., Pullman, B., Eds.; Reidel: Dordrecht, Holland, 1974; p 17. (15) Pulay, P. I n Modern Theoretical Chemistry; Schaefer, H. F., Ed.; Plenum: New York 1977; Vol. 4, p 153. (16) Brooks, E. R.; Laidig, W.D.; Saxe, P.; Goddard, J. D.; Yamaguchi, Y.; Schaefer, H. F. J . Chem. Phys. 1980, 72,4652. Rice, J. E.;Amos, R. D.; Handy, N. C.; Lee, T. J.; Schaefer, H. F. J . Chem. Phys. 1986, 85, 963. (17) Baker, J . J . Comput. Chem. 1986, 7, 385. (18) Saxe, P.; Yamaguchi, Y.; Schaefer, H. F. J . Chem. Phys. 1982, 77,
(IO) Pittman, C. U.; Kispert, L. D.; Patterson, T. E.J. Phys. Chem. 1973, 77. 494. ( I I ) Lucchini, V.; Modena, G.;Csizmadia, I. G.Gazz. Chim. Ifal. 1975, 105, 675. (12) Kollman, P.; Nelson, S.; Rothenberg, S. J . Phys. Chem. 1978, 82, 1403. (13) Dewar, M. J. S.; Rzepa, H. S. J . Comput. Chem. 1983, 4, 158.
5647. (19) Huzinaga, S. J. Chem. Phys. 1965, 42, 1293. (20) Dunning, T. H. J . Chem. Phys. 1970, 53, 2823. (21) Dunning, T. H.; Hay, P. J. In Modern Theoretical Chemistry; Schaefer, H. F.; Ed.; Plenum: New York, 1977; Vol. 3, p I . (22) Bauschlicher, C. W.; Schaefer, H. F.; Bagus, P. S. J . Am. Chem. Soc. 1977, 99, 1048. (23) McLean, A. D.; Chandler, G. S. J . Chem. Phys. 1980, 72, 5639.
2178.
0002-7863/91/lS13-7147%02.50/043 1991 American Chemical Society
7148 J . Am. Chem. SOC.,Vol. 113, No. 19, 1991
Hamilton and Schaefer
Table I. Absolute Energies (+535.0) in hartrees and Relative Energies in kJ/mol (in Parentheses) for C2H2Clt DZ+d CISD(+DZ SCF DZ+d SCF TZ2P SCF DZ+d CISD" Q) TZ2P CISD" TZ2P CISD(+Q)
A
-0.876 649 (103.3) tsb 3771 -0.896 657 (50.7) min -0.91 5 978
H.c-c,H
c\/"'
H-c-
H
H;c-c
-CI
(0.0)
H
min -0.871 491 (116.8) ts 8051
H+-cOc'
'I!
-0.947 067 (1 12.0) ts 1021 -0.957 067 (85.7) min -0.989 723 (0.0) min -0,951 796 (99.6) ts 3891
-1.012 166 (95.7) min -1.015 544 (86.9) min -1.048616
(0.0)
min -1.01 1650 (97.1) ts 3691
-1.306 228 ( 100.1)
-1.349463 (97.9)
-1.409 146 (86.9)
-1.460069 (84.2)
-1.300 404 (1 15.4)
-1.341 176 (1 19.7)
-1.399 586 ( I 12.0)
-1.447 655 (116.9)
-1.344 340 (0.0)
-1.386 758 (0.0)
-1.442 225 (0.0)
-1.492 155 (0.0)
Seven frozen core orbitals and three frozen virtuals. bTransition states are characterized by their imaginary vibrational frequency.
Table 11. Absolute Energies (+2648.0) in hartrees and Relative Energies in kJ/mol (in Parentheses) for C,H,Brt DZ SCF DZ+d SCF TZ2P SCF DZ+d CISD"
A H/c--c,H H-C-c H ' H, ,C-C-8r H
H/c-c'
81
/'I H-C-C'
H
-0.764 428 (93.9) tsb 3271 -0.778 571 (56.8) min -0,80021 1 (0.0) min -0.755 494 (117.4) ts 7751
-0.857 135 (70.3) min -0.855 536 (74.5) min -0.883 903 (0.0) min -0.848910 (91.9) ts 3631 -0.855 522 (74.5) ts 64i
-0.884 746 (73.3) min
-0.9 12 653 (0.0) min -0.879581 (86.8) ts 3491'
DZ+d CISD(+Q)
-1.200 394 (59.1)
-1.242123 (57.9)
-1.184 I69 (101.7)
-1.224 274 (106.3)
-1.222 919 (0.0)
-1.264 179 (0.0)
"Sixteen frozen core orbitals and seven frozen virtuals. bTransition states are characterized by their imaginary vibrational frequency. TZ contraction of the Br 15s12p primitive set given above [to (15sl2p/IOs8p)] with the contraction coefficients given in ref 24. The polarization function exponents for the TZ2P set were specified as q ( C ) = 1.5,0.375;ad(CI) 3 1.5,0.375;ad(&) 0.54,0.19; and ap(H) = 0.75.
Results and Discussion Energetics. C2H2Cl+. Previous studies on the C2H2CI+ion primarily focused on the relative energies of the chlorenium and the 2-chlorovinyl structures, with the conclusion that the open 2-chlorovinyl isomer is preferred. The STO-3G S C F difference is 18.4 kJ/mol on the basis of partially optimized geometries,12 and from DZ-quality S C F computations, these differences range from 42 to 54 k J / ~ n o l . ~ * MNDO ~ * ~ I * ~places ~ the chlorovinyl cation 35.6 kJ/mol above the chlorenium ion." The 1-chlorovinyl global minimum, which would result directly from Markovnikov protonation of chloroacetylene, is found to be so in all theoretical studies. Predictions of the energy difference between the 1- and 2-chlorovinyl cations are less variable, from 49 to 57 kJ/mol for MNDO, STO-3G SCF, and DZ-quality SCF. The above results (see Table I) are consistent with those from our D Z S C F predictions. The vibrational frequencies reveal that the bridged ion is a transition state for the motion of the CI atom between equivalent 2-chlorovinyl cations, with a 52.6 kJ/mol classical energy barrier. The 2-chlorovinyl cation is a minimum at this level of theory, as is the I-chlorovinyl ion. A transition state for the interconversion of H C C H C P and H2CCCI+ is located on the potential energy surface in a region that indicates that an H atom and the CI atom are simultaneously moving (see Figure 1). This is reminiscent of the C2H3+surface, in which a similar motion occurs with a much smaller barrier.26 This latter sta(24) Scuseria, G.E.; Duran, M.; Maclagan, R.G.A. R.;Schaefer, H. F. J . Am. Chem. SOC.1986, 108, 3248. (25) Olah, G.A. Halonlum fons; Wiley: New York, 1975.
tionary point is the highest energy point of major interest on the D Z S C F hypersurface. The situation dramatically changes even upon adding polarization functions on the heavy atoms. While the stationary points retain their minimum or saddle point character, the 2-chlorovinyl cation increases in energy with reference to the global minimum. The two transition states are stabilized and destabilized until the chlorine-bridged transition state is the highest point on the surface. With our largest basis set, the chlorenium ion becomes a minimum at the S C F level of theory. Searches to find the saddle points connecting the ring isomer of C2H2CI+to the neighboring minima at the TZ2P S C F level of theory were unsuccessful. Upon inclusion of electron correlation into the wave function, only three stationary points were found. In spite of the lack of harmonic vibrational frequencies for these stationary points, we are convinced that the ring and I-chlorovinyl structures are definitely minima and that the 2-chloro isomer is probably a higher energy minimum. The CISD and CISD(+Q) energies reveal that electron correlation preferentially stabilizes the bridged isomer by about 12 kJ/mol, not an unexpected result. This effect should be sufficient to change the DZ+d S C F transition state to a DZ+d CISD minimum. There is no question that the 1-chlorovinyl cation is a minimum, whereas the potential energy hypersurface around the 2-chlorovinyl cation was probed by finite displacements of the C-C-CI and C-C-H bends. At the TZ2P CISD level, the finite displacement of the C-C-CI angle by f O . O O 1 rad increases the energy by 3.3 X lo-' hartree, and the simultaneous displacement of the C-C-CI and C-C-H angles by *0.001 rad increases the energy by 2.1 X lo-' hartree. The latter displacements at the DZ+d CISD level increase the energy relative to the DZ+d CISD (26) Lindh, R.;Roos, B. 0.;Kraemer, W. P. Chem. fhys. Lerr. 1987, 139, 407.
Do the Vinyl Isomers of CzHzCl+ and CzH2Br+ Exist?
1.074 1.069 1.083
J . Am. Chem. SOC.,Vol. 113, No. 19, 1991 1149
1.073 1.069
1'07>c
1.243 1.237 1.265 1.252
H
L\H
H
165.3" 164.8" 164.1" 163.8"
1.274 1.263 1.286 1.269
1.232 1.241
L\H 164.7"
1.264
164.5' 163.0"
1.276
1.571 1.570 1.567 1.568
1.730 1.729 1.723
1.289
C
C1
C l2O.00
1.082 1.093 1.087
190.00
1.075
191.00 190'60
1.233 1.232
1.645 1.655
157.9' 153.2"
c1
1.074
158.3"
188.6'
1.230
122.6" 122.10
H
1.601 1.811
/;i
CT
1 180.80 8 72 5.4 3'
121.90 12 05 9.6 3'
181.4'
123.3' 1.283
1.073 1.086 1.079
1.271 1.289 1.273
1'42.3"
\!
119.6" 1.158 1.145 1.124
Br
1.685 1.719
1.886
119.8'
H -1.076 m
Br
1.083 1.082 1.093
176.6"
112.3'
120.40
1.088 1.085 1.091 1.094
1.075 1.080 \
DZ+d SCF 7Z2P SCF
H Br
DZ+d CISD 7Z2P CISD
Figure 1. Optimized geometries for the structural isomers of C2H2CI+ investigated in this paper. Bond lengths are in angstroms. The level of theory at which the parameters are optimized follows the order given at the bottom of the figure. For example, if two bond lengths are given for a structure, they are DZ+d SCF and TZZP SCF optimized distances.
stationary point by 3.5 X IO-' hartree. This procedure of using finite displacements along probable transition vectors in no way guarantees that the 2-chlorovinyl structure is a minimum. The apparently increasing flatness of the potential energy surface does suggest that the 2-chlorovinyl cation is less favored at higher levels of theory. In fact, the chlorine-bridged ion is clearly lower in energy than the 2-chlorovinyl ion, with the best estimate of the energy difference being 33 kJ/mol in favor of the nonclassical ion. Thus the situation has been completely reversed from the D Z SCF level of theory. C2H2Br+. For C2H2Br+,S C F theory with small basis sets is again found to be inadequate. At the D Z S C F level, C2H2Br+ is seen to be much like C2H2CI+in its energetic properties (see Table II), with a slightly more stable bridged structure that remains a transition state. The addition of d functions to heavy atoms even more radically affects the energy than for C2H2CI+. The bromenium ion is already a minimum at the DZ+d S C F level of theory, lower than the 2-bromovinyl cation, which is located in an extremely shallow potential well. Upon the improvement
t.S.
1.075
DZ+d SCF TZ2P SCF DZ+d CISD
Figure 2. Geometrical parameters for the optimized geometries of the structural isomers of C2H2Brt found in this work. Bond lengths are in angstroms. The levels of theory at which the structural parameters are optimized are given at the bottom of the figure. For example, if two bond lengths are given for a structure, they are DZ+d SCF and TZZP SCF optimized distances.
of the basis set to TZZP, no stationary point could be found that resembles a 2-bromovinyl cation. Thus it is possible that there are only the three stationary points on the potential energy surface for in-plane motion of the H and Br atoms about the C-C backbone. Treatment of electron correlation with a DZ+d basis set leads to three stationary points for C2H2Br+ that resemble those for C2H2CI+(see Figure 2), except that the Br-bridged ion is only
7150 J . Am. Chem. Soc., Vol. 113, No. 19, 1991
Hamilton and Schaefer
58 kJ/mol above the global minimum, whereas the 2-bromovinyl cation is now 49 kJ/mol above the cyclic structure! The energy of the nonclassical ion relative to the open isomers is lower for the brominated forms than for the CI-substituted isomers, a trend that is seen in halogen additions to alkenes and alkynes (see ref 1, p 483, and ref 25); Le., bridged ions are more likely to be intermediates for addition of heavier halogens. The 2-bromovinyl cation also appears to be a C I S D minimum from simultaneous finite displacements of the C-C-Br and C-C-H angles by f0.001 rad to give energy increases of 7.5 x IOm8 hartree, an indication of a shallower minimum than that found for the 2-chlorovinyl cation. Comparison to C2H3+,C2H2F+,and C2H4Br+. Comparisons with C2H2F+are difficult to make, since the highest level theory in the literature to date is of D Z S C F quality. The ordering of the structural isomers from previous theoretical work gives the 1-fluorovinyl cation as the global minimum, the 2-fluorovinyl cation 67 kJ/mol higher? and the three-membered ring at 151 k J / m ~ l . ~ *It*is clear that more advanced ab initio computations will lower the energy of the cyclic structure, but probably not to the point that it becomes a minimum or lower than that of either fluorovinyl form. Examinations of the parent C2H3+potential surface have been made at high levels of theory, so we can estimate the qualitative effect of better wave functions. Incorporation of higher level excitations improves the relative energy of the nonclassical ion by 3 kJ/mol, and enlarging the basis set also lowers the relative energy of the bridged ion ~lightly.~'Basis sets need to be more complete for the heavier atoms, so the effect will be somewhat larger for the halenium ions. These high-level studies on C2H3+ have also obtained the transition state for the motion of the H atoms around the C=C bond.26 This movement is much more facile in the C2H3' system than in the corresponding halovinyl systems, since all of the C2H3+stationary points are within 19 kJ/mol of each other. The behavior of CzHzBr+ (and presumably C2H2CI+) is markedly different from that of the corresponding halonium ion system, C2H4Br+. The bromonium ion is the global minimum with the I-bromoethyl cation only 11 kJ/mol higher in energy.28 It is well-known that halonium ions form more easily than bridged intermediates from halogen addition to alkynes and that reaction rates for halogen addition to alkenes are usually orders of magnitude faster.* The formation of the 2-bromoethyl cation, which is the saturated analogue of the 2-bromovinyl cation, is so unfavorable that it takes less energy to undergo a 1,2 hydrogen shift to create the I-bromoethyl cation. Stabilization Energies. The stabilization of a carbocation by a substituent X (relative to H ) can be taken as the negative of the energy for the reaction
C2H3X
+ CzH3+
+
CzH2X'
+ CzH4
(1)
Of course, the most stable structure is used in computing this quantity, so the vinyl cations C2H3+ and C2H2X+have classical structures at the levels of theory employed. Using SCF energies with the DZ+d basis set, we obtain stabilization energies of 17 kJ/mol for CI and 33 kJ/mol for Br; Le., the right-hand side of eq 1 is favored. Upon an increase of the basis set size to TZZP, the S C F stabilization energies change to 20 and 35 kJ/mol for CI and Br, respectively. Therefore, increasing the basis set further will probably have little effect. The effect of electron correlation was determined with the DZ+d basis by using a supermolecule approach (the CISD energies of the two fragments on either side of eq 1 are computed by using a supermolecular system of the two fragments separated by IOOOO au) because of the well-known size-consistency errors in truncated CI. The stabilization energies increase to 30 kJ/mol for CI and 52 kJ/mol for Br when electron correlation is included. The most reliable values arise from utilizing the Davidson-corrected CISD energies to obtain stabi-
lization energies of 35 and 59 kJ/mol for CI and Br, respectively. These results are contrary to those expected on the basis of the negutiue stabilization energies for F and CI from early ~ t u d i e s . ~ J ~ Therefore, the stabilization energy for F is probably not as negative as previously thought. Geometries. The structural parameters for the optimized geometries are shown in Figures l and 2. The three-membered-ring structures of C2H2C1+and C2H2Br+are very similar. They resemble strong A complexes in that the acetylene-derived portion is slightly bent away from the halogen and the C-C bond is lengthened from that of acetylene by 0.05 A (DZP CISD gives a C - C bond distance of 1.213 A for C2H2t9). The C-Br distance is about 0.015 A longer in the bromenium ion than in the bromonium ion (DZ+d CISD C-Br distance of 2.025 AZ8),an indication of weaker bonding for bridged C2H2X+when compared to C2H4X+. The difference in carbon-halogen bond distance from that of a single bond is greater for cyclic CzHzCl+than for cyclic C2H2Br+,which is consistent with the idea that the CI atom is repelled more by the out-of-plane A bond since the CI atom must get closer to carbon to form a bond. The 1-halovinyl cation geometries also share common features, except for the C-X bond of course. The C-C bond is longer than in the cyclic arrangement discussed above, as it in no way can be viewed as a complexed acetylene. The DZ+d S C F C-Br bond is 0.21 A shorter than the typical single-bond length of 1.94 A. A small part of this difference is the usual tendency of SCF theory to give bond lengths too short if reasonable basis sets are used, but most of it results from the use of sp hybrid orbitals by the carbon to which the Br is bonded and from A back-donation of lone-pair electron density into the empty orbital on carbon. The DZ+d S C F C-Cl bond distance is 0.20 l s h o r t e r than the typical C-CI length of 1.77 A, for identical reasons. The C-H bond distances are increased because some of the C-H bond density is used to stabilized the empty p orbital through hyperconjugation. The hydrogen-bridged stuctures are transition states and are hence more variable. The only exception is the inclusion of the DZ+d CISD 2-bromovinyl cation, which appears to be a shallow minimum from finite displacements. Its likeness to the transition state leads us to conjecture that the 2-bromovinyl isomer may actually become a transition state at high levels of theory or from interactions with solvent. These hydrogen-bridged C2H2X+geometries resemble protons complexed to haloacetylenes. The A cloud is polarized toward the halogen, so the H atom is mostly on that side. This is not to maintain that proton addition will result in anti-Markovnikov addition, however. Most of the shortening of the C-X bond lengths is due to sp-sp3 orbital overlap, since A bonding involving halogen is not feasible. The geometries that bear a likeness to 2-bromovinyl cations are found only at the DZ+d S C F level, both a minimum and a transition state. Given their extreme closeness in energy, their structural similarities make sense. Of the 2-chlorovinyl structures (all apparently minima) the DZ+d CISD structure seems anomalously different from the others. However, the H-C-CI angle is consistent with the others. The H-C-X angle seems to hold at about 120' for all of the 2-halovinyl and the hydrogen-bridging geometries. A final note to make on the 2-halovinyl isomers is that the C-H bond to the carbocation center is significantly shorter than the other C-H bond, which is expected to stabilize the cation via hyperconjugation. This hyperconjugation and the variation in hybridization account for the differences. Frequencies. Harmonic vibrational frequencies for the minima found a t the TZ2P S C F level of theory are presented in TabIe 111. The halenium ions are very similar, both in their vibrational frequencies and in the more sensitive IR intensities. The only modes that can be used to easily distinguish the two are the lower frequency modes involving halogen motion. The predicted IR intensities are large enough to warrant optimism about observing them (keeping in mind that S C F vibrational frequencies are typically 10%too high). The symmetric C-CI stretch is at a higher
~~~
(27) Liang, C.; Hamilton, T.P.;Schaefer, H. F. J . Chem. Phys. 1990,92, 3653. (28) Hamilton. T. P.;Schaefer, H.F. J . Am. Chem. Soc. 1990,112,8260.
(29) Gallo, M . M.; Hamilton, T.P.; Schaefer, H. F. J . Am. Chem. SOC. 1990, l1Z9 8714.
Do the Vinyl Isomers of C2H2Cl+and C2H2Br+Exist?
J . Am. Chem. SOC.,Vol. 113, No. 19, 1991 7151
Table 111. TZ2P SCF Harmonic Vibrational Frequencies in cm-l and IR Intensities in km/mol (in Parentheses) for the TZ2P SCF Minima of
C2H2CI+and C2H2Brt
sym CH
asym CH CC str asym rock sym rock
trans wag cis wag sym CX asym CX
3501 (29) 3412 (334) 1956 (13) 1002 (16) 991 (7) 817 (0) 807 (108) 598 (54) 63 (25)
3504 (38) 3416 (331) 1961 (18) 952 (23) 954 (6) 801 (0) 810 (105) 468 (32) 187 (24)
asym CH sym CH CC str CH2 scissor CH2 wag CH2 rock CX str CCX bend oop CCX bend ip
frequency than the C-Br stretch, but the asymmetric C-CI stretch (essentially opening the three-membered ring) vibrates at a lower frequency. This is yet another sign of the bromenium ion being more stable than chlorenium, because the bromenium ion’s higher asymmetric C-X stretching frequency reflects a deeper potential well, especially when the greater mass of Br is considered. If one is interested in detecting shifts in acetylene vibrational frequencies upon halenium ion formation, comparisons of Table 111 values with literature TZ2P S C F values for acetylene30 reveal that C-H stretching frequencies should decrease by 180 cm-I, the C-C stretch should be lowered by 250 cm-I, and the C-H rocking modes should increase by 1 30-1 70 cm-’ for chlorenium or 80-1 20 cm-’ for bromenium. The C-H wagging vibrations produce little repulsion, so it is no surprise that those frequencies are shifted upward only slightly from acetylene bending modes. The vibrational frequencies of the 1-halovinyl cations also resemble each other except for modes involving significant halogen motions. The C-X stretches have reasonable IR intensities and, hence, should be detectable at about 730 cm-’ for C-CI and 590 cm-I for C-Br. The vibrational frequencies for the normal modes that do not contain much halogen motion bear similarities to ethene vibrations. The following D Z P S C F ethylene vibrations3’ can be compared to the I-halo frequencies in Table 111: 3400 and 3100 cm-’ for average C-H stretches, 1817 cm-I for C-C stretching, 147 1 cm-’ for the CH, scissors mode, 1080 cm-l for the averaged CH, wag, and 887 cm-’ for the appropriate rocking vibration. The 2-chlorovinyl cation is a minimum on the TZ2P S C F surface, but the 2-bromovinyl ion is not. The 2-chlorovinyl cation is lower in energy than the chlorenium ion; therefore it is to be expected that the C-C-CI bending frequency is higher; Le., the local minimum for the classical structure is deeper than the one for the nonclassical ion. The C-H rocking modes are in the range found above in the chlorenium and I-chlorovinyl cation, and the C-CI stretch is similar to that of the I-chlorovinyl structure. The C-H stretching modes are separated by 200 cm-I, which correlates (30) Simandiras, E. D.; Rice, J. E.; Lee, T. J.; Amos, R. D.; Handy, N . C . J . Chem. Phys. 1988, 88, 3187. (31) Lee, T. J.; Allen, W.D.;Schaefer, H.F. J . Chem. Phys. 1987,87, 7062.
H\
H
,c-c-CI H
H
3322 (115) 3223 (181) 1969 (183) 1422 (15) 1006 (55) 892 (6) 815 (80) 364 (6) 356 ( I )
3320 (106) 3222 (190) 1932 (139) 1416 (17) 1013 (52) 864 (3) 648 (61) 326 (7) 331 (1)
;c-c--B,
H-C-c,
P H
CH str CH str CC str CH rock CH rock CH wag CX str CH wag CCX bend
3421 (259) 3237 (122) 1770 (3) 1233 (4) 1037 (20) 880 (31) 794 (14) 565 (104) 180 (12)
with the difference in TZ2P S C F bond lengths of 0.012 A. The wagging vibrations are decoupled, with the low-frequency wag involving the carbocation center. This difference in wagging frequencies is consistent with the idea that a favorable hyperconjugative stabilization of the carbocation center will be lost if the C-H bond partly responsible is bent out of the molecular plane. Surprisingly, the C-C stretch is 200 cm-l lower than for the other two C2H2CI+minima! This correlates with the .TZ2P S C F bond lengths; the actual C-C stretching frequencies for the C2H2CI+ isomers will not be so different, judging from the smaller gap between CISD values for C-C bond lengths, based upon Badger’s rule.
Conclusions The 1-halovinyl isomers of C2H2CI+and C2H2Br+are the global minima, which is not surprising, since significant ?r donation can occur to stabilize the empty p orbital on the carbocation center. What is unexpected is that the halenium ion is preferred over the 2-halovinyl cation for X = CI and Br. This is only evident at more advanced levels of a b initio theory, however. It may be possible that very high level theory or certain experimental conditions may cause the minimum for the 2-bromovinyl cation to disappear. The barrier between the bridged ion and the 1-halovinyl ion is significant, so either form should be isolable. The presence of the double bond in bromenium destabilizes the cyclic ion relative to the 1-bromo structure by 70 kJ/mol, when compared to energy differences in C2H4Brt. The stabilization energies for CI and Br and 36 and 55 kJ/mol, respectively. Given that the stabilization energy is negative for CI at low levels of theory, it is demonstrated that the stabilization energy for F is not as negative as previously supposed, either. Harmonic vibrational frequencies are presented (along with IR intensities) with the hope that they will be measured by experiment. Acknowledgment. This research was supported by the US. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Fundamental Interactions Branch (Grant DE-FG09-87ER138 1 1). Registry No. I-Chlorovinyl cation, 66202-71-9; I-bromovinyl cation, 135257-59-9; 2-chlorovinyl cation, 57847-84-4; 2-bromovinyl cation, 135257-60-2.
